Functional Muscle Networks as Biomarkers of Post-Stroke Motor Impairment and Therapeutic Responsiveness

  1. David O’Reilly
  2. Giorgia Pregnolato
  3. Andrea Turolla
  4. Pawel Kiper
  5. Ioannis Delis
  6. Giacomo Severini

  • Curated by eLife

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    eLife Assessment

    This important work employed a recent functional muscle network analysis to evaluate rehabilitation outcomes in post-stroke patients. While the research direction is relevant and suggests the need for further investigation, the strength of evidence supporting the claims is incomplete. Muscle interactions can serve as biomarkers, but improvements in function are not directly demonstrated, and the method's robustness is not benchmarked against existing approaches.

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Abstract

Standardised assessment of post-stroke motor impairment and treatment responsiveness remains a major clinical challenge. In this study, we tackle this challenge by applying a novel muscle network analysis framework to stroke survivors undergoing intensive upper-limb motor training. Our approach revealed distinct patterns of redundant and synergistic muscle interactions, collectively reflecting the diverse biomechanical roles of flexor- and extensor-driven networks. From these patterns, we derived new biomarkers that stratified patients by impairment severity and therapeutic responsiveness, each associated with unique physiological signatures. Notably, we identified a shift from redundancy to synergy in muscle coordination as a hallmark of effective rehabilitation—a transformation supported by a more precise quantification of treatment outcomes over conventional approaches. These findings offer an in-depth functional characterisation of post-stroke motor recovery and establish a robust, independent tool for evaluating rehabilitation efficacy.

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  1. eLife

    eLife Assessment

    This important work employed a recent functional muscle network analysis to evaluate rehabilitation outcomes in post-stroke patients. While the research direction is relevant and suggests the need for further investigation, the strength of evidence supporting the claims is incomplete. Muscle interactions can serve as biomarkers, but improvements in function are not directly demonstrated, and the method's robustness is not benchmarked against existing approaches.

  2. eLife

    Reviewer #1 (Public review):

    While the revised manuscript includes additional methodological details and a supplementary comparison with conventional NMF, it would be great if the authors could add the point below as limitations in the manuscript or change the title and abstract accordingly, since core issues remain:

    (1) The study claims to evaluate rehabilitation outcomes without demonstrating that patients actually improved functionally

    (2) The comparison with existing methods lacks the quantitative rigor needed to establish superiority

    (3) The added value of this complex framework over much simpler alternatives has not been demonstrated

    The strength of evidence supporting the main claims remains incomplete. I would encourage the authors to consider discussing these points

    (1) including or adding a limitation section about functional outcome measures that go beyond clinical scale scores, (2) providing/discussing quantitative benchmarks showing their method outperforms alternatives on specific, predefined metrics, and (3) clarifying the clinical pathway by which these biomarkers would inform treatment decisions.

    There are specific, relatively minor points, that require attention

    The authors write: "we did not focus on such complementary evidence in this study." This is a weakness for a paper claiming to provide "biomarkers of therapeutic responsiveness." The FMA-UE threshold defines responders, but there's no independent validation that patients actually functioned better in daily life. Can you please clarify?

    Maybe I missed the exact point about this, but with the added NMF plot, the authors list 'lower dimensionality' among their framework's advantages, but the basis for this claim is not clear because given that 12 network components were extracted compared to 11 "conventional" synergies. Can you please clarify, as it is not clear. You claim 'lower dimensionality' as an advantage of the proposed framework (in the Supplementary Materials), yet you extracted 12 components (5 redundant + 7 synergistic networks) compared to 11 synergies from the conventional NMF approach, which does not support a clinical / outcome advantage of this method. Please clarify.

  3. eLife

    Reviewer #2 (Public review):

    This study presents an important analysis of how interactions between muscles can serve as biomarkers to quantify therapeutic responses in post-stroke patients. To do so, the authors employ an information-theoretical metric (co-information) to define muscle networks and perform cluster analysis.

    I thank the authors for improving the clarity of the Methods section; the newly added Figure 5 is very helpful.

    One minor suggestion is that the authors should avoid overloading the notation "m" for both the EEG measurement and the matrix of II values (Eq. 1.1), which I now realise was the source of some of my initial confusion. I suggest that the authors use separate notation for these two quantities.

  4. eLife

    Author response:

    The following is the authors’ response to the original reviews.

    Public Reviews:

    Reviewer #1 (Public review):

    Summary:

    This study addresses an important clinical challenge by proposing muscle network analysis as a tool to evaluate rehabilitation outcomes. The research direction is relevant, and the findings suggest further research. The strength of evidence supporting the claims is, however, limited: the improvements in function are not directly demonstrated, the robustness of the method is not benchmarked against already published approaches, and key terminology is not clearly defined, which reduces the clarity and impact of the work.

    Comments:

    There are several aspects of the current work that require clarification and improvement, both from a methodological and a conceptual standpoint.

    First, the actual improvements associated with the rehabilitation protocol remain unclear. While the authors report certain quantitative metrics, the study lacks more direct evidence of functional gains. Typically, rehabilitation interventions are strengthened by complementary material (e.g., videos or case examples) that clearly demonstrate improvements in activities of daily living. Including such evidence would make the findings more compelling.

    We thank the reviewer for their careful consideration of our work. We agree that direct evidence for the functional gains achieved by patients is important for establishing the efficacy of a clinical intervention and that this evidence should provide comprehensive insights for clinicians, from videos to case examples as suggested. Our aim here was apply a novel computational framework to a cohort of patients undergoing rehabilitation, and in doing so, provide empirical support for its utility in standardised motor assessments. We have shown that our novel approach can identify distinct physiological responses to VR vs PT conditions across the post-stroke cohort (see Fig.2B and associated text). Hence, although the data contains virtual reality vs. conventional physical therapy experimental conditions which likely holds important insights into the clinical use case of virtual reality interventions, we did not focus on such complementary evidence in this study. In future work, research groups (including our own) investigating the important question of clinical intervention efficacy will likely gain unique and useful mechanistic insights using our approach.

    Moreover, a threshold of 5 points at the FMA-UE was considered as MCID, to distinguish between responder and non-responder patients, which represents an acknowledged and applicable measure in the clinical field. The use of single cases represents low evidence of change from the perspective of expert clinicians, raising concerns on the clinical meaningful of reported results. All this given, we chose to provide stronger evidence of clinical effect (i.e. comparison between responders and non-responders) interpreted from the perspective of muscle synergies, than to support our results in single selected cases, representing a bias in terms of translation to population of people survived to a stroke.

    Second, the claim that the proposed muscle network analysis is robust is not sufficiently substantiated. The method is introduced without adequate reference to, or comparison with, the extensive literature that has proposed alternative metrics. It is also not evident whether a simpler analysis (e.g., EMG amplitude) might produce similar results. To highlight the added value of the proposed method, it would be important to benchmark it against established approaches. This would help clarify its specific advantages and potential applications. Moreover, several studies have shown very good outcomes when using AI and latent manifold analyses in patients with neural lesions. Interpreting the latent space appears even easier than interpreting muscle networks, as the manifolds provide a simple encoding-decoding representation of what the patient can still perform and what they can no longer do.

    To address the reviewers concerns regarding adequate evidence for the claims made about the presented framework, we have now included an application of the conventional muscle synergy analysis approach based on non-negative matrix factorisation to the post-stroke cohort (see Supplementary materials Fig.5 and associated text). We made efforts to make this comparison as fair as possible by applying the conventional approach at the population level also and clustering the activation coefficients using a similar yet more conventional approach, agglomerative clustering. Accompanying the output of this application, we have included several points of where our framework improves significantly upon conventional muscle synergy analysis:

    “Comparison with conventional approaches

    To more directly illustrate the advantages of the proposed framework, we carried out a standardised pre-processing of the EMG data in line with conventional muscle synergy analysis. This included rectification, low-pass filtration (cut-off: 20Hz) and smooth resampling of EMG waveforms to 50 timepoints. All data for each participant at each session was separately normalised by channel-wise variance, concatenated together and input into non-negative matrix factorisation (NMF) ('nnmf' Matlab function, 10 replications) to extract 11 muscle synergies (W1-11 of Supplementary Materials Fig.5(Left)) and their time-varying activations. The number of components to extract was determined in a conventional way as the number of components required to explain >75% of the data variance. The extracted muscle synergies included distinct shoulder- (e.g. W2), elbow (e.g. W8) and forearm-level (e.g. W1) muscle covariation patterns along with more isolated muscle contributions (e.g. UT in W3, TL in W10).

    Regarding the clustering results of our framework and how they compare to conventional approaches, to facilitate this comparison we applied agglomerative clustering to the time-varying activation coefficients of all participants, trials, tasks separately for pre- and post-sessions and employed the 'evalclusters' Matlab function (Ward linkage clustering, Calinski Harabasz criterion, Klist search = 2:21) for each session. We identified two clusters both at pre-session (Criterion = 1.69) and post-session (Criterion = 1.81) as optimal fits to the population data (see Supplementary Materials Fig.5(Right)). We found no associations between pre- or post-session cluster partitions and participants FMA-UE scores. Nevertheless, we did identify significant associations between the pre-session clustering’s and S_Pre (X2 = 7.08, p = 0.008) and between post-session clustering’s and conventionally-defined treatment responders (X2 = 4.2, p = 0.04). These findings, along with the similar two-way clustering structure found using the NIF, highlights important commonalities between these approaches.

    To summarise the main advantages of our framework over this conventional approach:

    - Lower dimensionality and enhanced interpretability of extracted components.

    Our framework yields a lower number of population-level components that correspond more consistently to meaningful biomechanical and physiological functions.

    - Integration of pairwise muscle relationships.

    By incorporating muscle-pair level analysis, our framework captures coordinated interactions between primary and stabilising muscles—relationships that conventional NMF approaches overlook.

    - Separation of task-relevant and task-irrelevant activity.

    The NIF isolates task-relevant coordination patterns, distinguishing them from task-irrelevant interactions driven by biomechanical or task constraints. On the other hand, task-relevant and -irrelevant muscle contributions are intermixed in conventional muscle synergy analysis.

    - Ability to identify complementary functional roles.

    The NIF characterises whether muscle pairs act in similar or complementary ways, providing richer insight into motor control strategies.

    - Reduced dependence on variance-based optimisation.

    Unlike conventional methods that rely on maximising variance explained, our framework allows detection of subtle but functionally significant interactions that contribute less to total variance.

    - Improved detection of clinically relevant population structure.

    The clustering component of our framework revealed distinct post-stroke subgroups with important clinical relevance, distinguishing moderately and severely impaired cohorts and treatment responders and non-responders from pre-treatment data.”

    This supplementary analysis is referred to in the Methods section of the main text with reference to previous similar comparisons between our framework and conventional approaches:

    “Towards finding an effective approach to clustering participants in this data based on differences in impairment severity and therapeutic (non-)responsiveness, we found that conventional clustering algorithms (e.g. agglomerative, k-means etc.) could not provide substantive outputs (see Supplementary Materials Fig.5 and associated text for a direct comparison with conventional approaches), perhaps resulting from the complex interdependencies between the modular activations.”

    “To facilitate comparisons with existing approaches, we performed a conventional muscle synergy analysis on the post-stroke cohort (see Supplementary Materials Fig.5 and associated text). Further comparisons with conventional approaches can be found in our previous work (O’Reilly & Delis, 2022).”

    Further, we have also referred to a previous analysis of this post-stroke dataset using the conventional approach in the discussion section, where we point out how our approach can identify salient features of post-stroke physiological responses that conventional approaches cannot:

    “Further, the NIF demonstrated here an enhanced capability over traditional approaches to identify these crucial patterns, as earlier work on related versions of this dataset could not identify any differentiable fractionation events across the cohort (Pregnolato et al., 2025).”

    Overall, the utility of conventional muscle synergy analysis is well recognised across the field (Hong et al 2021). Our proposed approach builds on this conventional method by addressing key limitations to further enhance this clinical utility. We also agree that manifold learning approaches are an exciting area of research that we aim to incorporate into our framework in future research. Specifically, manifold learning methods like Laplacian eigenmaps can readily be applied to the co-membership matrix produced by our clustering algorithm, exploiting the geometry of this matrix to provide a continuous rather than discrete representation of population structure. We have highlighted this possibility in the discussion section:

    “Indeed, in future work, we aim to apply manifold learning approaches to the co-membership matrix derived from this clustering algorithm, providing a continuous representation of the population structure.”

    Third, the terminology used throughout the manuscript is sometimes ambiguous. A key example is the distinction made between "functional" and "redundant" synergies. The abstract states: "Notably, we identified a shift from redundancy to synergy in muscle coordination as a hallmark of effective rehabilitation-a transformation supported by a more precise quantification of treatment outcomes."

    However, in motor control research, redundancy is not typically seen as maladaptive. Rather, it is a fundamental property of the CNS, allowing the same motor task to be achieved through different patterns of muscle activity (e.g., alternative motor unit recruitment strategies). This redundancy provides flexibility and robustness, particularly under fatiguing conditions, where new synergies often emerge. Several studies have emphasized this adaptive role of redundancy. Thus, if the authors intend to use "redundancy" differently, it is essential to define the term explicitly and justify its use to avoid misinterpretation.

    We appreciate the reviewers concerns regarding the terminology employed in this study. Indeed, we agree that redundancy is seen in the motor control literature as a positive feature of biological systems, appearing to contradict the interpretations of the redundancy-to-synergy information conversion result we have presented. We also wish to highlight that across the motor control literature and beyond, the idea of redundancy is often conflated with the related but distinct notion of degeneracy. Traditional motor control research has also recognised this difference, for example, Latash has outlined this difference in the seminal work on motor abundance (https://doi.org/10.1007/s00221-012-3000-4). A key reference discussing this conflation and these two concepts in an information-theoretic way is found here: https://doi.org/10.1093/cercor/bhaa148. To summarise what their arguments mean for our work:

    - System degeneracy relates to the ability of different system components to contribute towards the same task in a context-specific way.

    - System redundancy corresponds to the degree of functional overlap among system components.

    Hence, conceptually speaking, informational redundancy as employed in our study (i.e. functionally-similar muscle interactions) links with system redundancy in that it quantifies the functional overlap of system components. This definition of system redundancy implies that it is an unavoidable by-product of degenerate systems (inefficient use of degrees of freedom) which should be minimised where possible. As a result of stroke, in our study and related previous work patients displayed increased informational redundancy, linking with the abnormal co-activations they typically experience for example and with previous results from traditional muscle synergy analysis showing fewer components extracted as a function of motor impairment post-stroke (i.e. higher informational redundancy) (Clark et al. 2010). Our novel contribution here is to convey how effective rehabilitation is underpinned by a redundancy-to-synergy information conversion across the muscle networks, relating in a loose sense conceptually to a reduction in system redundancy and enhancement of system degeneracy (i.e. functionally differentiated system components contributing towards task performance).

    Together, and alongside the mathematical descriptions of redundant (functionally-similar) and synergistic (functionally-complementary) information in what types of functional relationships they capture, we believe the intuition behind this finding has clear links with previous research showing a) the merging of muscle synergies in response to post-stroke impairment (i.e. functional de-differentiation), b) reduction in abnormal couplings with effective rehabilitation (i.e. functional re-differentiation). To communicate this more clearly to readers, we have included the following in the corresponding discussion section:

    “Previous research has shown that functional redundancy increases post-stroke (Cheung et al., 2012; Clark et al., 2010), reflecting the characteristic loss of functional specificity (i.e. functional de-differentiation) of muscle interactions post-stroke. Enhanced synergy with treatment here thus reflects the functional re-differentiation of predominantly flexor-driven muscle networks towards different, complementary task-objectives across the seven upper-limb motor tasks performed (Kim et al., 2024b), leading to improved motor function among responders.”

    Finally, we have screened the updated manuscript for consistent use of terminology including functional/redundant/synergistic.

    References

    Clark DJ, Ting LH, Zajac FE, Neptune RR, Kautz SA. Merging of healthy motor modules predicts reduced locomotor performance and muscle coordination complexity post-stroke. Journal of neurophysiology. 2010 Feb;103(2):844-57.

    Hong YN, Ballekere AN, Fregly BJ, Roh J. Are muscle synergies useful for stroke rehabilitation?. Current Opinion in Biomedical Engineering. 2021 Sep 1;19:100315.

    Latash ML. The bliss (not the problem) of motor abundance (not redundancy). Experimental brain research. 2012 Mar;217(1):1-5.

    O'Reilly D, Delis I. Dissecting muscle synergies in the task space. Elife. 2024 Feb 26;12:RP87651.

    Sajid N, Parr T, Hope TM, Price CJ, Friston KJ. Degeneracy and redundancy in active inference. Cerebral Cortex. 2020 Nov;30(11):5750-66.

    Reviewer #2 (Public review):

    Summary:

    This study analyzes muscle interactions in post-stroke patients undergoing rehabilitation, using information-theoretic and network analysis tools applied to sEMG signals with task performance measurements. The authors identified patterns of muscle interaction that correlate well with therapeutic measures and could potentially be used to stratify patients and better evaluate the effectiveness of rehabilitation.

    However, I found that the Methods and Materials section, as it stands, lacks sufficient detail and clarity for me to fully understand and evaluate the quality of the method. Below, I outline my main points of concern, which I hope the authors will address in a revision to improve the quality of the Methods section. I would also like to note that the methods appear to be largely based on a previous paper by the authors (O'Reilly & Delis, 2024), but I was unable to resolve my questions after consulting that work.

    I understand the general procedure of the method to be: (1) defining a connectivity matrix, (2) refining that matrix using network analysis methods, and (3) applying a lower-dimensional decomposition to the refined matrix, which defines the sub-component of muscle interaction. However, there are a few steps not fully explained in the text.

    (1) The muscle network is defined as the connectivity matrix A. Is each entry in A defined by the co-information? Is this quantity estimated for each time point of the sEMG signal and task variable? Given that there are only 10 repetitions of the measurement for each task, I do not fully understand how this is sufficient for estimating a quantity involving mutual information.

    We acknowledge the confusion caused here in how many datapoints were incorporated into the estimation of II. The number of datapoints included in each variable involved was in fact no. of timepoints x 10 repetitions. Hence for the EMGs employed in this analysis with a sampling rate of 2000Hz, the length of variables involved in this analysis could easily extend beyond 20,000 datapoints each. We have clarified this more specifically in the corresponding section of the methods:

    “We carried out this application in the spatial domain (i.e. interactions between muscles across time (Ó’Reilly & Delis, 2022)) by concatenating the 10 repetitions of each task executed on a particular side (i.e. variables of length no. of timepoints x 10 trials) and quantifying II with respect to this discrete task parameter codified to describe the motor task performed at each timepoint for each trial included.”

    In the previous paper (O'Reilly & Delis, 2024), the authors initially defined the co-information (Equation 1.3) but then referred to mutual information (MI) in the subsequent text, which I found confusing. In addition, while the matrix A is symmetrical, it should not be orthogonal (the authors wrote ATA = I) unless some additional constraint was imposed?

    We thank the reviewer for spotting this typo in the previous paper describing a symmetric matrix as ATA = I which is in fact related to orthogonality instead. To clarify this error, in the current study we have correctly described the symmetric matrix as A = AT here:

    “We carried out this application in the spatial domain (i.e. interactions between muscles across time (Ó’Reilly & Delis, 2022)) by concatenating the 10 repetitions of each task executed on a particular side (i.e. variables of length no. of timepoints x 10 trials) and quantifying II with respect to this discrete task parameter codified to describe the motor task performed at each timepoint for each trial included. This computation was performed on all unique mx and my pairings, generating symmetric matrices (A) (i.e. A = AT) composed separately of non-negative redundant and synergistic values (Fig.5).”

    Regarding the reviewers point about the reference to MI after equation 1.3 of the previous paper where co-Information is defined, we were referring both to the task-relevant and task-irrelevant estimates analysed there collectively in a general sense as ‘MI estimates’ as they both are derived from mutual information, task-irrelevant being the MI between two muscles conditioned on a task variable (conditional mutual information) and task-relevant being the difference between two MI values (co-I is a higher-order MI estimate). This removed the need to continuously refer to each separately throughout the paper which may in its own way cause some confusion. For clarity, in the results of that paper we also provided context for each MI estimate on how they were estimated (see beginning of “Task-irrelevant muscle couplings” and “Task-redundant muscle couplings” and “Task-synergistic muscle couplings” results sections), referring throughout the Venn diagrams depicting them (see Fig.1 of previous paper). In the present study however, for brevity and focus we did not perform an analysis on task-irrelevant muscle interactions and so decided to focus our terminology on co-I (II), a higher-order MI estimate. We acknowledge that this may have caused some confusion but highlight the efforts made to communicate each measure throughout the previous and present study. We have explicitly pointed out this specific focus on task-dependent muscle couplings in this paper at the end of the introduction of the updated manuscript:

    “To do so, here we focussed our analysis on quantifying task-dependent muscle couplings (collectively referred to as II), extracting functionally-similar (i.e. redundant) and -complementary (i.e. synergistic) modules…”

    (2) The authors should clarify what the following statement means: "Where a muscle interaction was determined to be net redundant/synergistic, their corresponding network edge in the other muscle network was set to zero."

    We acknowledge this sentence was unclear/misleading and have now clarified this statement in the following way:

    “This computation was performed on all unique mx and my pairings, generating sparse symmetric matrices (A) (i.e. A = AT) composed separately of non-negative redundant and synergistic values (Fig.5).” Additionally, we have now included an additional figure (fig.5) describing this text graphically.

    (3) It should be clarified what the 'm' values are in Equation 1.1. Are these the co-information values after the sparsification and applying the Louvain algorithm to the matrix 'A'? Furthermore, since each task will yield a different co-information value, how is the information from different tasks (r) being combined here?

    We thank the reviewer for their attention to detail. For clarity, at the related section of Equation 1.1, we have clarified that the input matrix is composed of co-I estimates:

    “The input matrix for PNMF consisted of the sparsified A on both affected and unaffected sides from all participants at both pre- and post-sessions concatenated in their vectorised forms. More specifically, the input matrix composed of redundant or synergistic values was configured such that the set of unique muscle pairings (1 … K) on affected and unaffected sides (maff and munaff respectively)…”.

    The co-I estimates in this input matrix are indeed those that survived sparsification in previous steps, however, for determining the number of modules to extract using the Louvain algorithm, this step has no direct impact or transformation on the co-I estimates and is simply employed to derive an empirical input parameter for dimensionality reduction. We refer the reviewer to the following part of this paragraph where this is described:

    “The number of muscle network modules identified in this final consensus partition was used as the input parameter for dimensionality reduction, namely projective non-negative matrix factorisation (PNMF) (Fig.1(D)) (Yang & Oja, 2010). The input matrix for PNMF consisted of the sparsified A on both affected and unaffected sides from all participants at both pre- and post-sessions concatenated together in their vectorised form.”

    Finally, as the reviewer has mentioned, the co-I estimates from the same muscles pairings but for different tasks, experimental sessions and participants are indeed different, reflecting their task-specific tuning, changes with rehabilitation and individual differences. To combine these representations into low-dimensional components, we employed projective non-negative matrix factorisation (PNMF). As outlined in the previous paper and earlier work on this framework (O’ Reilly & Delis, 2022), application of dimensionality reduction here can generate highly generalisable motor components, highlighting their ability to effectively represent large populations of participants, tasks and sessions, while allowing interesting individual differences mentioned by the reviewer to be buffered into the corresponding activation coefficients. These activation coefficients are for this reason the focus of the cluster analyses in the present study to characterise the post-stroke cohort. We have explicitly provided this reason in the methods section of the updated manuscript:

    “We focussed on $a$ here as the extraction of population-level functional modules enabled the buffering of individual differences into the space of modular activations, making them an ideal target for identifying population structure.”

    (4) In general, I recommend improving the clarity of the Methods section, particularly by being more precise in defining the quantities that are being calculated. For example, the adjacency matrix should be defined clearly using co-information at the beginning, and explain how it is changed/used throughout the rest of the section.

    We thank the reviewer for their constructive advice and have gone to lengths to improve the clarity of the methods section. Firstly, we have addressed all the reviewers comments on various specific sections of the methods, including more clearly the ‘why’ and ‘how’ of what was performed. Secondly, we have now included an additional figure illustrating how co-information was quantified at the network level and separated into redundant and synergistic values (see Fig.5 of updated manuscript). Finally, we have re-structured several paragraphs of the methods section to enhance flow with additional subheadings for clarity.

    (5) In the previous paper (O'Reilly & Delis, 2024), the authors applied a tensor decomposition to the interaction matrix and extracted both the spatial and temporal factors. In the current work, the authors simply concatenated the temporal signals and only chose to extract the spatial mode instead. The authors should clarify this choice.

    The reviewer is correct in that a different dimensionality reduction approach was employed in the previous paper. In the present study, we instead chose to employ projective non-negative matrix factorisation, as was employed in a preliminary paper on this framework (O’Reilly & Delis, 2022). This decision was made simply based on aiming to maintain brevity and simplicity in the analysis and presentation of results as we introduce other tools to the framework (i.e. the clustering algorithm). Indeed, we could have just as easily employed the tensor decomposition to extract both spatial and temporal components, however we believed the main take away points for this paper could be more easily communicated using spatial networks only. To clarify this difference for readers we have included the following in the methods section:

    “The choice of PNMF here, in contrast to the space-time tensor decomposition employed in the parent study (O’Reilly & Delis, 2024), was chosen simply to maintain brevity by focussing subsequent analyses on the spatial domain.”

    References

    Ó’Reilly D, Delis I. A network information theoretic framework to characterise muscle synergies in space and time. Journal of Neural Engineering. 2022 Feb 18;19(1):016031.

    O'Reilly D, Delis I. Dissecting muscle synergies in the task space. Elife. 2024 Feb 26;12:RP87651.

    Recommendations for the authors:

    Reviewing Editor Comments:

    Both reviewers are concerned with the manuscript in its current form. They questioned the relevance of the current approach in providing functional or mechanistic explanations about the rehabilitation process of post-stroke patients. Our eLife Assessment would change if you include comparisons between your current method and classical ones, in addition to improving the description of your method to strengthen the evidence of its robustness.

    Reviewer #1 (Recommendations for the authors):

    There is a minor typographical error in Figure 2 ("compononents" should be corrected).

    This error has been rectified.

    Reviewer #2 (Recommendations for the authors):

    The authors should be able to address most of my concerns by providing a substantially improved version of the Methods section.

    See above responses to the reviewers comments regarding the methods section.

    However, I would like the authors to explain in full detail (potentially including a simulation or power analysis) the procedure for estimating the co-information quantity, and to clarify whether it is robust given the sample size used in this paper.

    We refer the reviewer to our previous responses outlining with greater clarity the number of samples included in the estimation of co-I. We would also like to mention here that our framework does not make inferences on the statistical significance of individual muscle couplings (i.e. co-I estimates). Instead, these estimates are employed collectively for the sole purpose of pattern recognition. Nevertheless, to generate reliable estimates of the muscle couplings, we have employed a substantial number of samples for each co-I estimate (>20k samples in each variable) addressing the reviewers main concern her.

  5. Version published to 10.7554/elife.108509.2 on eLife
  6. Version published to 10.7554/elife.108509 on eLife
  7. Version published to 10.7554/elife.108509.1 on eLife
  8. eLife

    eLife Assessment

    This important work employed a recent, functional muscle network analysis for evaluating rehabilitation outcomes in post-stroke patients. While the research direction is relevant and suggests the need for further investigation, the strength of evidence supporting the claims is incomplete. Muscle interactions can serve as biomarkers, but improvements in function are not directly demonstrated, and the method's robustness is not benchmarked against existing approaches.

  9. eLife

    Reviewer #1 (Public review):

    Summary:

    This study addresses an important clinical challenge by proposing muscle network analysis as a tool to evaluate rehabilitation outcomes. The research direction is relevant, and the findings suggest further research. The strength of evidence supporting the claims is, however, limited: the improvements in function are not directly demonstrated, the robustness of the method is not benchmarked against already published approaches, and key terminology is not clearly defined, which reduces the clarity and impact of the work.

    Comments:

    There are several aspects of the current work that require clarification and improvement, both from a methodological and a conceptual standpoint.

    First, the actual improvements associated with the rehabilitation protocol remain unclear. While the authors report certain quantitative metrics, the study lacks more direct evidence of functional gains. Typically, rehabilitation interventions are strengthened by complementary material (e.g., videos or case examples) that clearly demonstrate improvements in activities of daily living. Including such evidence would make the findings more compelling.

    Second, the claim that the proposed muscle network analysis is robust is not sufficiently substantiated. The method is introduced without adequate reference to, or comparison with, the extensive literature that has proposed alternative metrics. It is also not evident whether a simpler analysis (e.g., EMG amplitude) might produce similar results. To highlight the added value of the proposed method, it would be important to benchmark it against established approaches. This would help clarify its specific advantages and potential applications. Moreover, several studies have shown very good outcomes when using AI and latent manifold analyses in patients with neural lesions. Interpreting the latent space appears even easier than interpreting muscle networks, as the manifolds provide a simple encoding-decoding representation of what the patient can still perform and what they can no longer do.

    Third, the terminology used throughout the manuscript is sometimes ambiguous. A key example is the distinction made between "functional" and "redundant" synergies. The abstract states: "Notably, we identified a shift from redundancy to synergy in muscle coordination as a hallmark of effective rehabilitation-a transformation supported by a more precise quantification of treatment outcomes."

    However, in motor control research, redundancy is not typically seen as maladaptive. Rather, it is a fundamental property of the CNS, allowing the same motor task to be achieved through different patterns of muscle activity (e.g., alternative motor unit recruitment strategies). This redundancy provides flexibility and robustness, particularly under fatiguing conditions, where new synergies often emerge. Several studies have emphasized this adaptive role of redundancy. Thus, if the authors intend to use "redundancy" differently, it is essential to define the term explicitly and justify its use to avoid misinterpretation.

  10. eLife

    Reviewer #2 (Public review):

    Summary:

    This study analyzes muscle interactions in post-stroke patients undergoing rehabilitation, using information-theoretic and network analysis tools applied to sEMG signals with task performance measurements. The authors identified patterns of muscle interaction that correlate well with therapeutic measures and could potentially be used to stratify patients and better evaluate the effectiveness of rehabilitation.

    However, I found that the Methods and Materials section, as it stands, lacks sufficient detail and clarity for me to fully understand and evaluate the quality of the method. Below, I outline my main points of concern, which I hope the authors will address in a revision to improve the quality of the Methods section. I would also like to note that the methods appear to be largely based on a previous paper by the authors (O'Reilly & Delis, 2024), but I was unable to resolve my questions after consulting that work.

    I understand the general procedure of the method to be: (1) defining a connectivity matrix, (2) refining that matrix using network analysis methods, and (3) applying a lower-dimensional decomposition to the refined matrix, which defines the sub-component of muscle interaction. However, there are a few steps not fully explained in the text.

    (1) The muscle network is defined as the connectivity matrix A. Is each entry in A defined by the co-information? Is this quantity estimated for each time point of the sEMG signal and task variable? Given that there are only 10 repetitions of the measurement for each task, I do not fully understand how this is sufficient for estimating a quantity involving mutual information.

    In the previous paper (O'Reilly & Delis, 2024), the authors initially defined the co-information (Equation 1.3) but then referred to mutual information (MI) in the subsequent text, which I found confusing. In addition, while the matrix A is symmetrical, it should not be orthogonal (the authors wrote AᵀA = I) unless some additional constraint was imposed?

    (2) The authors should clarify what the following statement means: "Where a muscle interaction was determined to be net redundant/synergistic, their corresponding network edge in the other muscle network was set to zero."

    (3) It should be clarified what the 'm' values are in Equation 1.1. Are these the co-information values after the sparsification and applying the Louvain algorithm to the matrix 'A'? Furthermore, since each task will yield a different co-information value, how is the information from different tasks (r) being combined here?

    (4) In general, I recommend improving the clarity of the Methods section, particularly by being more precise in defining the quantities that are being calculated. For example, the adjacency matrix should be defined clearly using co-information at the beginning, and explain how it is changed/used throughout the rest of the section.

    (5) In the previous paper (O'Reilly & Delis, 2024), the authors applied a tensor decomposition to the interaction matrix and extracted both the spatial and temporal factors. In the current work, the authors simply concatenated the temporal signals and only chose to extract the spatial mode instead. The authors should clarify this choice.

  11. Version published to 10.1101/2025.08.17.670726 on bioRxiv